Some aspects relating to the accuracy of high-order panel methods

• To verify that high order panels scheme do not generate spurious solution.
• The spurious is a direct consequence of low order schemes.
• It can be eliminated by preserving the circulation in the discretize scheme.
• Direct consequences on a moving boundary-high order does not exhibit spurious results.

In this study we have examined two numerical algorithms, based upon the high-order panels approach, to verify and demonstrate that a spurious solution is a direct result of a low-order scheme accuracy that violates the conservation of circulation. The first algorithm is based upon the parabolic Lagrange interpolation and the second one is based on the same parabolic Lagrange interpolation for the vortex sheet strength where the geometry of the body/foil is evaluated using a periodic cubic spline, mainly because the denominator in the integrand of the Cauchy algorithm is the main source of the numerical error in the scheme. Good agreement has been found between the computational and analytical results and a spurious free solution has been obtained for the high-order schemes, except for a spurious-like solution in the case of an under resolved problem.